I have (currently) a 3 server build (not including domain controllers):

SharePoint 2013 on Windows Server 2012 R2

SQL 2012 on Windows Server 2012 R2

Workflow Manager 1.0 Refresh on Windows Server 2012 R2

The SharePoint site collection is over http; and the Workflow manager endpoint is https.

The certificate is installed in the SharePoint server and is added under "Manage Trust"

Workflow Manager was initially installed on the SharePoint server; however it was later decided that it should be rolled out on its own server. Whilst it probably would have been a better idea to just leave the farms, then join them from the new server, I instead completely rebuilt the farms from scratch.

Workflow applications were removed from the SharePoint server:

Workflow Manager 1.0

Service Bus

Windows Fabric

(Workflow Manager Client 1.0 was left on the server; version is 2.0.40131.0, which matches the version that ends up on the workflow manager server)

The databases were dropped from the database server.
Workflow Manager 1.0 Refresh was then installed on the WFM server, with a service account used as the "Run As" account. The rest of the settings were left as default.

It took a while, but the Configuration Wizard ran with no errors.

The Workflow and service bus farm services are running (I had an issue with these earlier, which I thought might have been the cause, but no...)

However, when running the Register-SPWorkflowService powershell cmdlet, I am receiving the above error.

Running Fiddler at the time of registration shows the error occurs when calling the URL /SharePoint/$Activities. This call hangs for a very long time (much longer than powershell is willing to wait for it) and eventually returns 503 - Service Unavailable with the following message:

Waiting five minutes and trying again has not remedied the problem.

Examining the Event log on the Workflow Manager server also shows the problem:

Here it shows a call made to /$Activities (as opposed to /SharePoint/$Activities) and is sending a message to /WF_Management scope.

I have not been able to find any more information about this issue.

Can anyone identify what might be causing this timeout, and how I could resolve this issue?

I had the same issue when registering WFM on a SharePoint 2016 farm. My issue was that on Windows server 2016, the WFM farm wizard (powershell as well) is not granting the proper permissions to the WFM site. I had to grant them manually for the service account and the Domain Users after the WFM farm was created then it registered without issue. Hope that helps.

Since your SharePoint web application/site is running HTTP you should/must run the Register-SPWorkflowService cmdlet with the –AllowOAuthHttp. I am a bit surprised though that you get a timeout. Usually you get this error message:

Failed to query the OAuth S2S metadata endpoint at URI ...

Because you already executed the Register-SPWorkflowService cmdlet before, you should add the -AllowOAuthHttp and -Force switches.